In a classic pouring problem, given two unmarked jugs with capacities \(m\) and \(n\) pints, where \(m\) and \(n\) are relatively prime integers, and an unlimited supply of water, the goal is to obtain exactly \( p\) pints, where \( p\) is an integer, \( 0 < p < m+n \). This capsule uses properties of least residues to show that there are two distinct pouring sequences to achieve the desired result. The more efficient sequence can be determined by solving a linear congruence.

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